IPhone 6 issue Could not activate cellular data network?

I have a new iPhone 6, coming from an iPhone 4s. I have AT&T btw. In the top left it shows i have bars, and then the LTE or 4G symbol shows up, but when I try to use safari or anything web-based it says I'm not subscribed to a cellular data service, or "could not activate cellular data network". It works fine on Wi-Fi, but why won't it work on LTE or 4G.

Have you subscribe to a cellular data service? If the answer is affirmative, go to Settings>>General>> Reset>>Reset Network Settings to have a try.

If it doesn't work, continue to follow the guide below to active the activate cellular data:

Navigate to Settings -> Cellular and turn off "Cellular Data" and "Roaming", then navigate to Settings -> Safari and choose the option to "Clear all cookies and data"
Turn Wi-Fi off on the iPhone. Power the iPhone off and wait 5 minutes before turning it back on. At last, Navigate to Settings -> Cellular and turn on "Cellular Data" (you can turn on roaming if you want too).

If the issue still persists, do a "soft reset" and "hard reset" to your iPhone 6 Plus to try again. If it still doesn't work, send it to a professional.

Check over the APN settings for it. If that's OK, then check with AT&T about it.